Optimisation of Plate Thickness Using Finite Difference Method

Abstract

A finite difference numerical method of solving biharmonic equation is presented. The biharmonic equation and plate theory are used to solve a classical engineering problem involving the optimisation of plate thickness to minimise deformations and stresses in the plate. Matlab routines were developed to solve the resulting finite difference equations. The results from the finite difference method were compared with results obtained using ANSYS finite element formulation. Using the finite difference method, a plate thickness of 277 mm was obtained with a mesh size of 3 m and a plate thickness of 271 mm was obtained with a mesh size of 1 m., whiles using ANSYS finite element formulation, a plate thickness of 270 mm was obtained. The significance of these results is that, by using off-the-shelf general application tool and without resorting to expensive dedicated application tool, simple engineering problems could be solved.